Pauli reductions of supergravities in six and five dimensions.

The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, e.g., the S7 reduction of 11-dimensional supergravity, such a consistent "Pauli reduction" does exist. In this paper, we study this existence question in two examples of S² reductions of supergravities. We do this by making use of a relation between certain S² reductions and group manifold S³=SU(2) reductions of a theory in one dimension higher. By this means, we establish the nonexistence of a consistent S² Pauli reduction of five-dimensional minimal supergravity. We also show that a previously discovered consistent Pauli reduction of six-dimensional Salam-Sezgin supergravity can be elegantly understood via a group-manifold reduction from seven dimensions. [ABSTRACT FROM AUTHOR]